Simulation models are approximations of physical systems. If an actual physical system differs from its simulation model, management strategies designed using a model might not satisfy management goals in reality.
Simulation/Optimization (S/O) model accuracy is only as good as that of the employed simulation models. Because optimization may cause constraints to be tight, deterministic mathematically optimal strategies might not be very robust. In other words, a small difference between reality and model-assumed parameters could cause an optimization problem constraint to be violated in reality although it is satisfied in the model.
On the other hand, a reliable or robust solution strategy will achieve management goals in reality even if the physical system differs from the model. We disclose a practical way of increasing optimal solution strategy robustness without harming the objective function (OF) value, even if data concerning the real system is limited.
A ‘realization’ is an “assumed reality” or one set of physical system parameters assumed within a model. In chance-constrained programming (CCP), relations based on a probability distribution are incorporated as constraints in the optimization problem. The multiple realization approach (MRA) puts constraints of several different realizations into one optimization model. The optimization model satisfies all the constraints of all realizations simultaneously.
CCP and MRA are powerful mathematical tools for developing reliable strategies and for developing tradeoff curves for reliability versus desired solution parameters. However, both approaches have historically relied upon the ability to quantify random processes and establish a probability density function (PDF) for real system parameters. Accurately establishing a PDF requires a significant amount of real system data. For most real-world problems, cost prevents sufficient accurate data collection.
Sensitivity analysis provides insight into the robustness of a solution but does not tell how to make a solution more robust. Using trial-and-error to modify a solution to make it more robust is inefficient. Here we disclose a more efficient approach for improving solutions.
This Robustness Enhancing Optimizer (REO) incorporates sensitivity analysis within a S/O model to guide optimization. REO maximizes robustness for selected system parameters while maintaining a predetermined value for a primary OF (such as a least cost for a cost minimization problem).
Reliability evaluation and robustness evaluation both address parameter uncertainty by simulating response of different realizations to the same set of decision variables or stimuli. However, here we distinguish between robustness and reliability.
Reliability is determined by: (a) developing many alternative realities (realizations) of the study area by changing model assumptions stochastically based on a probability density function or statistically derived information; and then (b) simulating how a particular decision strategy affects the system represented by each realization (i.e., by running one simulation of the strategy per realization). If the results of a simulation satisfy all optimization problem constraints, the strategy is considered feasible for that realization. A decision strategy's reliability is the percentage of N-realizations that yield feasible results for that strategy (with N greater than 1).
A decision strategy's robustness is determined using deterministically created realizations. For example, a realization can be produced by multiplying a calibrated system parameter array set by an assumed factor smaller than 1 or larger than 1, respectively representing a systematic proportional reduction or increase in the array values. A strategy is considered feasible for that realization if the results of simulating the strategy satisfy all optimization problem constraints. A strategy's parameter robustness range is here defined as the range of parameter multipliers for the multi-layer calibrated parameter arrays for which the strategy will satisfy all constraints and retain the same objective function value.